1. A common metric to evaluate the performance of a model of a car is its "O to 60" time. That is, the amount of time it takes to go from rest to 60 miles per hour. Recently, the Porsche 918 Spyder hybrid supercar and Tesla Model S both managed times of 2.2 seconds. However, most of our vehicles do not have these capabilities. Dr. Lawrence's 2011 Chevrolet Impala is rated as having a 0 to 60 time of roughly 8 seconds. Instead of working with miles per hour, which cars do not need an entire mile to reach 60 miles per hour nor do they need an hour of time to reach that speed, converting to feet per second makes more sense as we know multiple feet will be traveled and it will be done in a matter of seconds. (Think of traveling on highway on-ramps.) Quite nicely, converting 60 miles per hour is exactly 88 feet per second. a. Assume that the speed of Dr. Lawrence's Impala increases linearly from rest (ie. constant positive acceleration) with a velocity function of v(t) = 11t [in ft/sec]. Write the definite integral for this journey with Dr. Lawrence's Impala. What type of measurement would be produced when evaluating this definite integral? b. Sketch the graph of v(t) on the graph below and shade the area underneath v(t) bounded by the proper interval. Label the axes appropriately.

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.